Fade a render layer to transparent
Probably the most effective way to fade in alpha is to use the alpha over node.

In the image below, the top color socket is set to completely transparent (I'll explain how to do this further down), and the image is put into the bottom color socket. The factor (the highlighted input) controls the opacity. 0 is 100% transparent, 1 is 100% opaque. 



It's the other way around if you switch the color inputs to make this image go in the top and the transparency in the bottom.

To make the color input completely transparent, just use the alpha slider in the color picker drop down. Make sure it's set to 0: